1) When you receive £80 bank interest, this is £100 from which £20 of income tax has already been deducted. When you complete your UK self assessment your bank interest of £100 will be added to your other income, the tax computed, and then a credit of £20 will be deducted from the tax bill for the tax already paid.
However, things are due to change in April 2016. From 6 April, 2015 UK banks will start to pay interest without any tax deduction. People with income in the basic rate band (paying 20% marginal rate) will have a personal savings allowance (PSA) of £1,000 interest tax free, and those in the higher rate band (paying 40% marginal rate) will have a PSA of £500. If your bank interest exceeds your tax free allowance then you will pay the tax in your self assessment.
2) You report the gross interest amount of £100 on 1040 Schedule B. You can reduce or eliminate US tax on it by filing IRS Form 1116 (passive) to take a tax credit for the £20 of UK tax already paid, and any further tax you will pay on it if you are a higher rate tax payer.
As remarked above, from April 2016, you will have no UK tax liability for the tax free allowance of £1,000 or £500. Depending upon your total UK interest, you may or may not see US tax on your bank interest. For example, if you are a basic rate tax payer and have only £1,000 interest, there will be no UK tax, but you will need to pay US tax at your US marginal rate on that £1,000. If you are a UK basic rate taxpayer and have £2,500 bank interest, you will have £300 UK tax, on the £1,500 above your allowance, and that can be taken as a credit against whatever US tax you would pay on £2,500.
As you can see, it will be fairly complicated to figure out, for the purposes of taking a credit using IRS Form 1116, exactly what UK tax you have paid on your UK bank interest in calendar year 2016. However, if your total circumstances are straightforward and your bank interest is only a few hundred pounds, then Form 1116 is probably something you can do yourself.